Essays | Many Shades of Scaling

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The Mouse to Elephant Curve – Dinner with Thomas Robert Malthus – The Kidney of Your Business – COVID-19 and the Intellectuals – In Case you are Wondering, Nero killed Saint Peter and Paul – Virtue-cum-Ethics Scaling


Friends, in this eclectic essay, I explored the implication of scaling in 1) metabolism/biology 2) business 3) demography 4) public health/epidemiology and finally in 5) economics and politics. Enjoy!


One. There is a saying that goes thus: “One Englishman makes a gentleman, two make a bet and three, a parliament. One Frenchman, makes a lady’s man, two makes a duel, three a Paris commune…” I have no idea where I stumbled on that quote, but it stuck with me ever since, and it might help us (conceptually) in this essay.

Two. What happens to the length and area of a square when you engage in some sort of scaling? Take a square that is twice as big as a smaller square x. While the length of the square will be twice as big as the length of the smaller square x, the area will not be twice as big but four times. And the relationship between these quantities remain (super)linear, no matter how big your square is.

Three. Another quote. “With my family, I’m a communist. With my close friends, I’m a socialist. At the state level of politics, I’m a Democrat. At higher levels, I’m a Republican, and at the federal levels, I’m a Libertarian.” This statement – by the Geoff and Vince Graham brothers – implicates the importance of thinking about scale when we talk politics (More on this later.)

In brief, the properties of systems/things/people/societies are revealed when they scale, in order words; we ask the question: how do systems respond when the ‘size’ changes. In this rather eclectic essay we will explore a few, and I will start with an example in the scientific domain, namely – metabolic scaling.

The Mouse to Elephant Curve

The Kleiber’s rule or what you might know as ¾ rule, states that the metabolic rate of an animal is proportional to the mass of the body raised to the power of three-quarter, mathematically expressed as the following:

Metabolic rate is indicative of how much energy you need to survive.  And if you happen to visit Mikumi National Park in Tanzania, and ask the zoo keeper for the average weight of a male African bush Elephant, she will say something like 6,000kg (~13,000lbs). Now, compare that, for example, with a very healthy Etruscan shrew mouse which weighs – on average – 2g (~0.004lbs).

Your intuition might lead you to believe that an elephant would need something like a million times more energy to survive compared to our shrew mouse. That is, if you by any chance, plot a graph of the metabolic rate on the vertical axis and body mass of animal on the horizontal axis (logarithm scale), what we are talking about here is a linear or a super-linear scaling (slope  1).

Surprisingly, after doing this comparison with several mammals, what Max Kleiber found was a sub-linear scaling (check graph below) This simply means: as the body mass of an animal increases, even though an increased energy level is required, they tend to use it more efficiently, thereby reducing total energy needed (a sublinear economy of scale). The curve has been dubbed the mouse to the elephant curve.

When things scale, our intuition suffers.

(Source: Science 04 Jun 1999: 284(5420). pp. 1607-1609, K. SCHMIDT-NIELSEN, SCALING: WHY IS ANIMAL SIZE SO IMPORTANT?)

The Kidney of Your Business

It shouldn’t surprise you then, friends, that a somewhat parallel line can be drawn between the aforementioned scaling and what you might observe in, say, business.

And I will illustrate, if you give me some time.

Let’s say I run a goat farm, for some reason, I just happen to be a goat farmer. I use to own ten goats and I spend $100 to feed each goat in a month. A friend of mine visited me one late night and told me how dumb I was sitting on ten goats all this while. He told me all about the gospel of scaling and whatnot – he said I should do such and such, and I did.

Now, friends, I have 100 goats and I spend only $45.273 to feed each goat every month. What good news!

In microeconomics, we call this economics of scale, as many of my readers might know (and the idea is ridiculously simple): as the volume of production increases, the cost of producing a unit of the product decreases (up to a point. Like most things in life, there are limits, where the cost snaps back up).

Source: Tidoni

And yet there is another flavor of this in business, something we could call informational advantage. Again, we could use an illustration: I travelled to this remote place with my friends for an adventure, let’s say to climb a huge mountain.

As expected from an amateur climber who had not worked out in ages, I had this head banging headache after the first climb. I took a stroll to a store nearby to buy a medication. The pharmacist offered the two headache medications that they had in stock. One is called sagena and the other zoba. I have heard about segena before, in fact segena happen to be the most common headache medication in this country.

But zoba – first time I heard that thing. And then I asked for the price, as I should. The attendant replied saying that sagena costs the equivalent of $20 and zoba $15. Friends, while I could save some $5 and just buy zoba, I felt my mouth (and gut) is a pretty personal place and why risk screwing it up for a bloody five bucks.

I went for sagena, and I climbed the next day. This is a benefit of scale (for sagena executives), except that, it is purely informational.

Dinner with Reverend Malthus

In his 1798 book – an essay on the principle of population by the 32-year-old population economist and clergyman Thomas Malthus. He argued that since it appears the world population will be growing at an exponential rate and food production from sedentary farming will only increase linearly, the world will end up in deep misery and hunger. This will force humans to a subsistence economy – hunting, gathering, garbage picking, social parasitism, artisan fishing, transhumance, that kind of thing. The last time I checked the history books Malthus was no prophet.

To quote Malthus directly:

Famine seems to be the last, the most dreadful resource of nature. The power of population is so superior to the power of the earth to produce subsistence for man that premature death must in some shape or other visit the human race.

Revd. Malthus’s dooms day  was about a century into the future, and little did he know I will be writing about scaling in 2020 while battling with a bowl of rice and vegetables as I ride along (save the COVID19 pandemic).

And here is where Malthus missed it, our grandmothers knew this very well: Necessity is the mother of invention.  He saw humans primarily as a liability not as a potential asset. When I talk about assets, I talk about the agricultural revolution, the industrial revolution, and the green revolution.

And what happens when we scale human population (to Malthus’s dismay)?

“Between 1900 and 2000, the global population quadrupled, from 1.6 to 6.1 billion, [while] grain production quintupled, from 400 million to 1.9 billion tons.”

Prof. Geoffrey West of the Santa Fe Institute has showed that, to paraphrase, if you home city is 15 times bigger than mine, innovation in my city will be less than 15 times smaller than yours – that is, innovation scales super linearly.

When things scale, some scientists (and Revds.) go burst! However, one must admit – while the exact prediction of Thomas Malthus was wrong – that there is such a thing called the point of no return (just like the limit in our little microeconomics lesson).

So far, we have discussed two modes of scaling – sublinear economy of scales that we see in biology (and business) plus the super linear scaling that we can observe in socio-economic activities. Now, let’s switch our focus to exponential scaling in epidemiology.

COVID-19 and Public Intellectuals

When the plague (COVID-19) came in, otherwise intelligent people, began to engage in reckless comparisons. Here is a dumb one: “more people die of car accidents compared to this flu”, and another, “more people die in their swimming pools”, signaling that it shouldn’t be taken seriously. And what might be the issue here? The issue is, you will be starting on a wrong foot when you compare apples and oranges. And I will even correct myself and say the following: you start on a wrong foot when you start comparing apples and squirrels – to show the folly of such comparisons once and for all.

An intelligent observer might have looked closely and categorize these things based on how they might scale, and only compare things that scales similarly. An airborne viral respiratory infection will scale exponentially, and this will naturally lead us to a fat-tailed distribution because of their multiplicative effects. On the other hand, causalities in swimming pools or road accidents will not. And all of these should make sense because no one gets infected with a road accident respiratory virus in rallies, labs, jam packed offices, or protests.

If I fall in my room and, God forbid, break my back. My neighbor is not more likely to fall in her room, talkless of breaking her back. However, to make such argument for a respiratory virus – that had knocked out thousands at the time – will be profoundly dumb.

In order words, if you leave proto-pandemics on unchecked, they start like play, and then suddenly all you get is pandemonium, New York city is a case in point, doing the initial months of the COVID19 pandemic in the United States.

What more? Let’s say someone argues back and says ‘what of the hindsight bias?’ We should reply and say: the whole point of predicting the future is not having to predict the future, as such.

And this is what I mean: when you have a respiratory virus in the air, with many deaths in China, anyone with any fat-tailed distribution intuitions left in them should panic, and shut down vulnerable connecting dots, say, fancy-colored planes flying all over the globe. Because, I repeat, when proto-pandemics go unchecked, they start like play, and then suddenly all you get is pandemonium.

The lack of understanding of this kind of scaling led to thousands of avoidable deaths in the initial months of the pandemic.

The way things scale, not the way they are, are often the most important thing. And when some things scale, sadly, people end up dead.

So far, we have considered how systems, diseases scale; we should now see what happens when we scale an individual, particularly when the power allotted to an individual scale up like mad.

To answer this question, it will worth our while to go back in time and revisit mortals that were afforded some of the greatest power on earth – the Roman emperors! It turns out that here, things are a little different, a little unpredictable. Let’s call this for lack of better words – political scaling.

In Case you are Wondering, Nero killed Saint Peter and Paul

Nero was a popular emperor in the Julio-Claudia dynasty, and he had a very busy reign during the time he spent with the ancient Romans – he started off by killing his own brother, Britannicus with the aid of his in-house toxicologist Gaul Locusta.

Locusta later got some sort of medal for her accomplishment including lands outside Rome. Nero power drunkenness was not something that will soon assuage, so he continued – in A.D. 59, he killed his mother, Agrippina. Agrippina was a powerful woman in the roman empire, she was a wife of an emperor (Claudius), sister to another (Caligula, a no less brutal emperor) and mother to one (Nero, himself). But this doesn’t stop Nero from matricide.

Still, he continues – around 62AD after impregnating a very beautiful woman the daughter of Titus Ollius – Poppaea Sabina – Nero took one step further and divorced and later killed his wife, Octavia.  Even Seneca, his praecipuus caritate, could not stop him.

Without boring the reader with more horror stories (and there is still much, much more), let me wrap this up – Nero was brutal.

And one wonders, is this not the position, the philosopher-king Marcus Aurelius held about a century later in 161 A.D.? An intellectual emperor, his book – Meditations – is one that will easily stun any mortal. And, he is not just the talking type, he gracefully eats his own cooking and I am sure Emperor Marcus will not have attempted to eat in any Roman restaurant whose chef have decided to eat elsewhere.

Even though he was plagued by poor health his entire life and had to endure the death of about four children. He preserved the empire.

Cassius Dio, the classic historian, like most people, was Marcus’s Fan:

“[Marcus] did not meet with the good fortune that he deserved, for he was not strong in body and was involved in a multitude of troubles throughout practically his entire reign. But for my part, I admire him all the more for this very reason, that amid unusual and extraordinary difficulties he both survived himself and preserved the empire”.

Did I mentioned that at some point when the empire finance was crumbling due to strains from incessant wars, that Marcus sold his imperial properties in the forum of Trojan so he can pay his soldiers? forgive me if I have not. He did.

And I will quickly add: Nero did the exact opposite, at least if we go by the account of Suetonius. On July 18 the year 64, Nero was believed to have started the great fire of Rome, to clear some land space for his palatial complex, the Domus Aurea. He sings and plays his lyre while Rome burnt (even though I have learnt that the lyre story is contentious).

Anyways, in the aftermath, he organized the first Roman empire persecution of Christians, blaming the fire on them. The persecution, some believed, lead to the death of Saint Peter and Paul.

The Torches of Nero

And Seneca (Nero’s chief of staff) practically stick his neck out in support of Nero’s sanity. (After all, why did the philosopher leave Corsica?)

You only need read what Seneca wrote in De Clementia in 65, assuring people that Nero could only get better, effectively a recommendation letter: “That which is undergirded by truth, and grows out of solid ground, becomes better and greater with the passage of time”, referring to his boss, Nero.

Going back to our theme: while there are no power laws for this type of scaling, no slope, no graphs. All we need remember is the words of the 19th century British politician Lord Acton: “Power tends to corrupt, and absolute power corrupts absolutely. Great men are almost always bad men.” While I can go on with Roman emperors like Caligula who slept with his officials’ wife and then brag about it publicly, these stories are plentiful across cultures.

To summarize with the main point, a sample size of one is too tiny – while Socrates objection to democracy is striking – a sample size of 10 million is better than one!

And for all Socrates fuss about democracy, he was a democrat in deeds but not in speech.

Virtue-cum-Ethics Scaling

Have you ever thought about why you cared so much about your daughter’s toothache than any magnitude of earthquakes in Japan and Ecuador combined? If you haven’t, I have news for you: ethics doesn’t scale. This is a point the philosopher Nassim Taleb had made in his books.

Talk about many of us who buy $5 coffee every now and then, while millions of folks are hungry because they can’t afford to live on $1 a day. Virtue doesn’t scale.

Talk about how you cuss your ‘friends’ on Facebook and twitter without even thinking about it. Virtue doesn’t scale.

The thing is, we tend to more well-behaved, kind, virtuous in smaller societies living face to face.

And as a Nigerian citizen, I have stories to tell. Take for starters, in 2014, the terrorist group Boko-Haram kidnapped some 276 girls from a secondary school in northern Nigeria, Chibok. As I write these words in October of 2020, many of them are either dead or still nowhere to be found.  Unsurprisingly, the main culprit for this is lack of skin in the game on the part of the leaders.

You see, Nigeria runs a massive centralized system of government with an aggressive top to bottom political philosophy. As such, ones’ wonder is tempered with regards the failure of the recovery of all the kidnapped girls, but more importantly, the failure of lack of security that led to their kidnap in the first place.

Let’s face it, to the politicians in Abuja (capital of Nigeria), those poor girls are just mere statistics. To their parents, friends, and community – an egregious tragedy.

And this will take me to my main point. Let’s attempt to reverse the system by simulating an aggressively decentralized system of government where decision is made at the bottom – essentially a bottom to top system. The odds of the Chibok incident happening will be very low. ‘Why?’, you ask. Because, the leaders of this small community live in that community, and that changes everything.

If the boss drinks the palm wine they drink, drive on the same road, go to the same church, lives two stones away, one has to dare the individual to f*** up. Because if he or she does, his head might be lifted up from his shoulders.

That aside, the chances of messing up is pretty damn low, because when you see sick people, homeless folks, parents of kidnapped kids, paralyzed children, with your two bloody eyes, there is a biological drive to effect change. But to reduce an individual to a tiny roman figure I on a giant spread sheet sitting in the cloud – bro, that doesn’t work!

And then that quote I promised to comment about, this is a nice junction to reintroduce it:

“With my family, I’m a communist. With my close friends, I’m a socialist. At the state level of politics, I’m a Democrat. At higher levels, I’m a Republican, and at the federal levels, I’m a Libertarian.”

This is scale in action, simply put: the larger the number of people aggregated in a system, the higher the chance someone will want to game the system, the higher the chance someone will want to behave badly, to cheat, to steal (recall some of the aforementioned comment on the importance of social contacts).

As such, the political and economic philosophy have to be finetuned differently for each scale. Kapish?

While communism is a fine idea for running your family, you don’t want to support trying it at higher level with crap load of people. It will end with disaster.

Closing Remarks

From geometry, biology, business, population theory, pandemics, economics to politics. When served with any system. Ask the simple questions: what happens when it gets bigger? What happens when it gets smaller?

Friends, if you do, I wager there will be a lot to unpack.

Thank you for reading.

© Olatomiwa Bifarin 2020


  • An Essay on the Principle of Population, Thomas Malthus, 1798.
  • Will the Earth Ever Fill Up? Adam Kucharski, 2015. Nautilus Magazine.
  • Marcus Aurelius, Wikipedia.
  • Dying everyday: Seneca at the Court of Nero, James Romm, 2014.
  • Urban Friction, Geoffrey West, 2012. The Economist.
  • Body size and metabolic rate, Max Kleiber, 1947. Physiological Reviews. 27 (4): 511–541.
  • Metabolic Rate and Kleiber Law
  • The Nero Really Fiddle while Rome burnt? Link
  • Lammers et al. PNAS July 14, 2020 117 (28) 16264-16266; Link 
  • Pasquale Cirillo and Nassim Nicholas Taleb, Nature Physics June 2020 16(606) 606–613
  • Science 04 Jun 1999: Vol. 284, Issue 5420, pp. 1607-1609. DOI: 10.1126/science.284.5420.1607 Link
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